The optical fibers are thin, thus, the light entering from one side of the wire surface has more chances to reflect back from the inside surface due to the larger angle of incidence.
The angle of the strike is large due to the small size of the wire and this angle is greater than the critical angle.
As the angle of the incident light on the inside surface is greater than the critical angle, thus, the total internal reflection of the takes place.
Hence, there are more chances of total internal reflection of light inside the optical fiber wire than the emergence of light through the wire.